anticoagulant: sodium citrate
Sodium citrate is the most accessible anticoagulant and the same anticoagulant that is used in labs for observing how blood clots. Since it is commonly used in cooking as an emulsifer for cheese sauces, it is very easy to find and pretty cheap.
Sodium citrate can refer to a few molecules but most commonly and what we are using it's trisodium citrate. Trisodium citrate for cooking will probably be trisodium citrate dihydrate which is perfectly acceptable, but if you like precision you should account for the fact that trisodium citrate dihydrate is heavier than anhydrous trisodium citrate.
When added to blood, the sodium ions dissociate from the citrate molecule, which chelates calcium in the blood, interrupting the clotting process.
A concentration of 0.109M sodium citrate is typically used in medical settings. Given trisodium citrate dihydrates molar mass of 294.1g/mol, that means 32.0g of trisodium citrate dihydrate is needed per liter of blood.
Blood that has had enough trisodium citrate to not coagulate will be unbearably salty. Necessarily, there will be a 0.327M (0.109M * 3, trisodium) concentration of sodium ions in blood that has had 0.109M trisodium citrate added. Given NaCl's molar mass of 58.44g/mol, that is the equivalent of 19.11g (58.44g * 0.327mol) per liter of blood. That's very salty! So if you want to put it in your mouth for any reason it will be an unpleasant experience.
Theoretically, the saltiness could be literally cut in third by using monosodium citrate. Anhydrous monosodium citrate has a molar mass of 214.1g/mol, so you would use 23.88g/liter, and would be equivalent to a more reasonable 6.37g NaCl/liter blood. It is basically unobtainium commerically, but is incredibly trivial to produce yourself by mixing solid citric acid with aqueous baking soda. Experiments to be conducted.
I also think there is a strong possibility that citric acid itself would work. They are buried in medical terms I don't understand so I don't know for sure, but some journal papers I have read seem to imply that citric acid has similar efficacy to citrate. Citric acid is already known to be a good chelating agent, so I would expect it to do the exact same thing and chelate the calcium in blood. Experiments to be conducted.